ts-project
xl
library(vars)
library(astsa)
library(forecast)
library(tseries)
library(dplyr)
library(ggplot2)
library(lubridate)
library(data.table)
library(ggpubr)# read data
df = read.table(file = '2004-2019.tsv', sep = '\t', header = TRUE)
df['X']=NULL
colnames(df) = c("start_date", "end_date","region", "state", "fuel", "num_gas_stations",
"unit", "avg_price","sd_price", "min_price","max_price","avg_price_margin",
"coef_dist","dist_avg_price","dist_sd_price","dist_min_price", "dist_max_price",
"coef_price", "year", "month")# rename the data
df = df %>% mutate(region = recode(region, "SUL"="South", "SUDESTE"="Southeast", "CENTRO OESTE"="Midwest",
"NORTE"="North", "NORDESTE"="Northeast"))
table(df$region)##
## Midwest Northeast North Southeast South
## 15429 36869 24702 17047 12776df = df %>% mutate(fuel = recode(fuel, "ÓLEO DIESEL"="Diesel", "GASOLINA COMUM"="Regular Gasoline", "GLP"="LPG", "ETANOL HIDRATADO"="Hydrous Ethanol", "GNV"="Natural Gas", "ÓLEO DIESEL S10"="Diesel S10"))
#table(df$fuel)
#df[df$fuel=='LPG',]colnames(df)## [1] "start_date" "end_date" "region"
## [4] "state" "fuel" "num_gas_stations"
## [7] "unit" "avg_price" "sd_price"
## [10] "min_price" "max_price" "avg_price_margin"
## [13] "coef_dist" "dist_avg_price" "dist_sd_price"
## [16] "dist_min_price" "dist_max_price" "coef_price"
## [19] "year" "month"# compute the average gas price
str(df)## 'data.frame': 106823 obs. of 20 variables:
## $ start_date : Factor w/ 785 levels "2004-05-09","2004-05-16",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ end_date : Factor w/ 785 levels "2004-05-15","2004-05-22",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ region : Factor w/ 5 levels "Midwest","Northeast",..: 1 1 1 1 2 2 2 2 2 2 ...
## $ state : Factor w/ 27 levels "ACRE","ALAGOAS",..: 7 9 11 12 2 5 6 10 15 17 ...
## $ fuel : Factor w/ 6 levels "Hydrous Ethanol",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ num_gas_stations: int 127 387 192 162 103 408 278 105 125 423 ...
## $ unit : Factor w/ 3 levels "R$/13Kg","R$/l",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ avg_price : num 1.29 1.16 1.39 1.26 1.18 ...
## $ sd_price : num 0.016 0.114 0.097 0.07 0.078 0.132 0.218 0.158 0.13 0.141 ...
## $ min_price : num 1.19 0.89 1.18 1.09 1.05 0.999 1.03 1.35 1.1 0.989 ...
## $ max_price : num 1.35 1.45 1.76 1.51 1.4 ...
## $ avg_price_margin: Factor w/ 11930 levels "-","0.001","0.022",..: 395 331 351 364 172 358 285 447 285 209 ...
## $ coef_dist : num 0.012 0.098 0.07 0.055 0.066 0.095 0.15 0.097 0.101 0.115 ...
## $ dist_avg_price : Factor w/ 15997 levels "-","0.506","0.547",..: 220 158 365 225 336 352 495 511 326 342 ...
## $ dist_sd_price : Factor w/ 5858 levels "-","0","0.001",..: 112 90 97 121 79 130 70 93 74 93 ...
## $ dist_min_price : Factor w/ 21620 levels "-","0.3257","0.326",..: 20 115 194 250 543 208 518 1408 580 203 ...
## $ dist_max_price : Factor w/ 22576 levels "-","0.5992","0.7044",..: 221 381 596 783 350 1303 1052 1367 1068 1329 ...
## $ coef_price : Factor w/ 397 levels "-","0","0.001",..: 135 117 100 145 84 136 64 84 79 98 ...
## $ year : int 5 5 5 5 5 5 5 5 5 5 ...
## $ month : int 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 ...df2 = df[,c("start_date" ,"fuel",'min_price'
,"max_price","avg_price","coef_dist","sd_price")]
df3= df2 %>%
group_by(start_date,fuel) %>%
summarise_all("mean")
df3## # A tibble: 4,263 x 7
## # Groups: start_date [785]
## start_date fuel min_price max_price avg_price coef_dist sd_price
## <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2004-05-09 Hydrous Eth… 1.10 1.70 1.34 0.0851 0.113
## 2 2004-05-09 Regular Gas… 1.86 2.34 2.09 0.0384 0.0809
## 3 2004-05-09 LPG 28.5 36.4 32.6 0.0477 1.55
## 4 2004-05-09 Natural Gas 1.10 1.15 1.13 0.0119 0.0131
## 5 2004-05-09 Diesel 1.32 1.61 1.44 0.0367 0.0529
## 6 2004-05-16 Hydrous Eth… 1.09 1.67 1.33 0.0863 0.114
## 7 2004-05-16 Regular Gas… 1.86 2.32 2.09 0.0409 0.0863
## 8 2004-05-16 LPG 28.7 37.0 32.6 0.0501 1.64
## 9 2004-05-16 Natural Gas 1.11 1.15 1.13 0.0111 0.0121
## 10 2004-05-16 Diesel 1.30 1.61 1.44 0.0377 0.0544
## # … with 4,253 more rowsunique(df3$fuel)## [1] Hydrous Ethanol Regular Gasoline LPG Natural Gas
## [5] Diesel Diesel S10
## 6 Levels: Hydrous Ethanol Regular Gasoline LPG Natural Gas ... Diesel S10df3[df3$fuel=='Regular Gasoline',]## # A tibble: 785 x 7
## # Groups: start_date [785]
## start_date fuel min_price max_price avg_price coef_dist sd_price
## <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2004-05-09 Regular Gas… 1.86 2.34 2.09 0.0384 0.0809
## 2 2004-05-16 Regular Gas… 1.86 2.32 2.09 0.0409 0.0863
## 3 2004-05-23 Regular Gas… 1.87 2.34 2.09 0.0416 0.0877
## 4 2004-05-30 Regular Gas… 1.87 2.33 2.10 0.0412 0.0873
## 5 2004-06-06 Regular Gas… 1.88 2.35 2.11 0.0394 0.0840
## 6 2004-06-13 Regular Gas… 1.88 2.40 2.14 0.045 0.0967
## 7 2004-06-20 Regular Gas… 1.97 2.44 2.22 0.0346 0.0774
## 8 2004-06-27 Regular Gas… 1.98 2.44 2.22 0.0350 0.0779
## 9 2004-07-04 Regular Gas… 1.99 2.46 2.22 0.0369 0.0817
## 10 2004-07-11 Regular Gas… 1.98 2.44 2.21 0.0371 0.0827
## # … with 775 more rowsdata visulization
# df3=df3[df3$fuel!="Diesel S10",]
df3$start_date = as.Date( df3$start_date)
library(RColorBrewer)
col_prod = brewer.pal(9,"BrBG")
vis1 = ggplot() +
geom_line(data = df3[df3$fuel=="Hydrous Ethanol",],aes(start_date, avg_price),col=col_prod[1]) +
geom_ribbon(data = df3[df3$fuel=="Hydrous Ethanol",],aes(x = start_date, ymax = max_price, ymin = min_price), alpha = 0.6, fill = col_prod[1])+ theme(axis.title.x=element_blank(), axis.text.x=element_blank(), axis.title.y=element_blank())
vis2 =ggplot() +geom_line(data = df3[df3$fuel=="Regular Gasoline",],aes(start_date, avg_price),col=col_prod[2]) +
geom_ribbon(data = df3[df3$fuel=="Regular Gasoline",], aes(x = start_date, ymax = max_price, ymin = min_price), alpha = 0.6, fill = col_prod[2])+ theme(axis.title.x=element_blank(), axis.text.x=element_blank(), axis.title.y=element_blank())
vis3 = ggplot() + geom_line(data = df3[df3$fuel=="Natural Gas",],aes(start_date, avg_price),col=col_prod[7]) +
geom_ribbon(data = df3[df3$fuel=="Natural Gas",], aes(x = start_date, ymax = max_price, ymin = min_price), alpha = 0.6, fill = col_prod[7])+ theme(axis.title.x=element_blank(), axis.text.x=element_blank(), axis.title.y=element_blank())
vis4 = ggplot() + geom_line(data = df3[df3$fuel=="Diesel",],aes(start_date, avg_price),col=col_prod[8]) +
geom_ribbon(data = df3[df3$fuel=="Diesel",], aes(x = start_date, ymax = max_price, ymin = min_price), alpha = 0.6, fill = col_prod[8]) + theme(axis.title.x=element_blank(), axis.text.x=element_blank(), axis.title.y=element_blank())
vis5 = ggplot() + geom_line(data = df3[df3$fuel=="LPG",],aes(start_date, avg_price),col=col_prod[3]) +
geom_ribbon(data = df3[df3$fuel=="LPG",], aes(x = start_date, ymax = max_price, ymin = min_price), alpha = 0.6, fill = col_prod[3])+ theme(axis.title.x=element_blank(), axis.text.x=element_blank(), axis.title.y=element_blank())
vis6 = ggplot() + geom_line(data = df3[df3$fuel=="Diesel S10",],aes(start_date, avg_price),col=col_prod[9]) +
geom_ribbon(data = df3[df3$fuel=="Diesel S10",], aes(x = start_date, ymax = max_price, ymin = min_price), alpha = 0.6, fill = col_prod[9])+ theme(axis.title.x=element_blank(), axis.text.x=element_blank(), axis.title.y=element_blank())
#scale_x_date(labels = lbls, breaks =brks)
ggarrange(vis1, vis2,vis5,vis4,vis3,vis6, labels = c("Hydrous Ethanol", "Regular Gasoline","LPG","Natural Gas","Diesel" ,"Diesel S10" ), ncol = 3, nrow = 2, font.label = list(size = 25, face = "bold"))
ggarrange(vis1, vis2,vis5,vis4,vis3, labels = c("Hydrous Ethanol", "Regular Gasoline","LPG","Natural Gas","Diesel" ), ncol = 3, nrow = 2, font.label = list(size = 25, face = "bold"))
# decompose
HE_ts=ts(df3[df3$fuel=="Hydrous Ethanol",]$avg_price,frequency=52)
RG_ts=ts(df3[df3$fuel=="Regular Gasoline",]$avg_price,frequency=52)
NG_ts=ts(df3[df3$fuel=="Natural Gas",]$avg_price,frequency=52)
LPG_ts=ts(df3[df3$fuel=="LPG",]$avg_price,frequency=52)
D_ts=ts(df3[df3$fuel=="Diesel",]$avg_price,frequency=52)
ts_list = c(HE_ts,RG_ts,NG_ts,LPG_ts,D_ts)
plot(decompose(HE_ts))
plot(decompose(RG_ts))
plot(decompose(NG_ts))
plot(decompose(LPG_ts))
plot(decompose(D_ts))
# decompose
HE_ts=ts(df3[df3$fuel=="Hydrous Ethanol",]$avg_price)
RG_ts=ts(df3[df3$fuel=="Regular Gasoline",]$avg_price)
NG_ts=ts(df3[df3$fuel=="Natural Gas",]$avg_price)
LPG_ts=ts(df3[df3$fuel=="LPG",]$avg_price)
D_ts=ts(df3[df3$fuel=="Diesel",]$avg_price)
# frequency analysis
sp=spectrum(HE_ts, log="no")
plot(sp,log='no',main="Periodogram for Hydrous Ethanol",xlim=c(0,0.5))
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])],sort(sp$spec,decreasing = T)[1],col=2)
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[2])],sort(sp$spec,decreasing = T)[2],col=2)
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[2])]+0.03,sort(sp$spec,decreasing = T)[2],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[2])]))
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]+0.03,sort(sp$spec,decreasing = T)[1],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]))
sp=spectrum(RG_ts, log="no")
plot(sp,log='no',main="Periodogram for Regular Gasoline",xlim=c(0,0.5))
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])],sort(sp$spec,decreasing = T)[1],col=2)
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[2])],sort(sp$spec,decreasing = T)[2],col=2)
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[2])]+0.03,sort(sp$spec,decreasing = T)[2],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[2])]))
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]+0.03,sort(sp$spec,decreasing = T)[1],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]))
sp=spectrum(NG_ts, log="no")
plot(sp,log='no',main="Periodogram for Natural Gas",xlim=c(0,0.5))
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])],sort(sp$spec,decreasing = T)[1],col=2)
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[3])],sort(sp$spec,decreasing = T)[3],col=2)
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[3])]+0.03,sort(sp$spec,decreasing = T)[3],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[3])]))
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]+0.03,sort(sp$spec,decreasing = T)[1],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]))
sp=spectrum(LPG_ts, log="no")
plot(sp,log='no',xlim=c(0,0.5),main="Periodogram for LPG")
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])],sort(sp$spec,decreasing = T)[1],col=2)
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[4])],sort(sp$spec,decreasing = T)[4],col=2)
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[4])]+0.03,sort(sp$spec,decreasing = T)[4],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[2])]))
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]+0.03,sort(sp$spec,decreasing = T)[1],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]))
sp=spectrum(D_ts, log="no")
plot(sp,log='no',xlim=c(0,0.5),main="Periodogram for Diesel")
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])],sort(sp$spec,decreasing = T)[1],col=2)
points(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[3])],sort(sp$spec,decreasing = T)[3],col=2)
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[3])]+0.03,sort(sp$spec,decreasing = T)[3],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[3])]))
text(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]+0.03,sort(sp$spec,decreasing = T)[1],paste(sp$freq[which(sp$spec==sort(sp$spec,decreasing = T)[1])]))
# function for extract the data
df4 = df3[df3$fuel=='Hydrous Ethanol',][,c('start_date','avg_price')]
df4=merge(df4,df3[df3$fuel=='Regular Gasoline',][,c('start_date','avg_price')],by='start_date')
colnames(df4)=c('start_date',"Hydrous Ethanol", "Regular Gasoline")
df4=merge(df4,df3[df3$fuel=='LPG',][,c('start_date','avg_price')],by='start_date')
df4=merge(df4,df3[df3$fuel=='Natural Gas',][,c('start_date','avg_price')],by='start_date')
df4=merge(df4,df3[df3$fuel=='Diesel',][,c('start_date','avg_price')],by='start_date')
colnames(df4) = c('start_date',"Hydrous Ethanol", "Regular Gasoline", "LPG","Natural Gas","Diesel" )
# which(df4$start_date == as.Date("2004-05-16"))
df4['group'] = c(rep(1,785-52),rep(2,52))
df4$start_date = as.Date( df4$start_date)
str(df4)## 'data.frame': 785 obs. of 7 variables:
## $ start_date : Date, format: "2004-05-09" "2004-05-16" ...
## $ Hydrous Ethanol : num 1.34 1.33 1.34 1.37 1.38 ...
## $ Regular Gasoline: num 2.09 2.09 2.09 2.1 2.11 ...
## $ LPG : num 32.6 32.6 32.6 32.5 32.6 ...
## $ Natural Gas : num 1.13 1.13 1.13 1.13 1.14 ...
## $ Diesel : num 1.44 1.44 1.44 1.44 1.44 ...
## $ group : num 1 1 1 1 1 1 1 1 1 1 ...# scale the data
df5 = data.frame( apply(df4[,2:6],2,scale))
df5['date'] = as.Date(df4[,1])
df5['group']=df4[,7]
# split df to two group, set last year data as the reference
df5_scaled = df5[df5$group==1,]
df5_scaled2 = df5[df5$group!=1,]
df5_scaled$group=NULL
# labels and breaks for X axis text
brks = df5_scaled$date[seq(1, length(df5_scaled$date),52)]
lbls = unique(lubridate::year(df5_scaled$date))
df5_scaled_melt <- reshape2::melt(df5_scaled, "date")
# plot
ggplot(df5_scaled_melt, aes(x=date)) +
geom_line(aes(y=value,col=variable)) +
labs(title="Scaled Average Gas Price",
y="Average Price",
color=NULL) + # title
scale_x_date(labels = lbls, breaks =brks) + # change to monthly ticks and labels
scale_fill_brewer( palette = 3) +
theme(legend.position="top")+theme_gray()
# turn off minor grid
# stl(ts(df5_scaled, frequency=52),
# s.window = "periodic") %>% plot
acf1=ggAcf(df5_scaled$Hydrous.Ethanol,200)
acf2=ggAcf(df5_scaled$Regular.Gasoline,200)
acf3=ggAcf(df5_scaled$LPG,200)
acf4=ggAcf(df5_scaled$Natural.Gas,200)
acf5=ggAcf(df5_scaled$Diesel,200)
ggarrange(acf1, acf2,acf3,acf4,acf5,
ncol = 1, nrow = 5)
# rename the prepared data
df5_diff = data.frame( apply(df5_scaled[,1:5],2,diff))
df5_diff['date'] = as.Date(df5_scaled[,1][-1])
df5_diff_melt = reshape2::melt(df5_diff, "date")
# plot
ggplot(df5_diff_melt, aes(x=date)) +
geom_line(aes(y=value,col=variable)) +
labs(title="Average gas price with first differencing",
y="Average Price",
color=NULL) + # title
scale_x_date(labels = lbls, breaks =brks) + # change to monthly ticks and labels
scale_fill_brewer( palette = 3) +
theme(legend.position="top")+theme_gray()
acf1=ggAcf(df5_diff$Hydrous.Ethanol,200)
acf2=ggAcf(df5_diff$Regular.Gasoline,200)
acf3=ggAcf(df5_diff$LPG,200)
acf4=ggAcf(df5_diff$Natural.Gas,200)
acf5=ggAcf(df5_diff$Diesel,200)
# rename the prepared data
df5_diff2 =df5_diff
df5_diff2$Hydrous.Ethanol = c(diff(df5_diff2$Hydrous.Ethanol),NA)
df5_diff2$LPG = c(diff(df5_diff2$LPG),NA)
df5_diff_melt2 <- reshape2::melt(df5_diff2, "date")
# plot
ggplot(df5_diff_melt2, aes(x=date)) +
geom_line(aes(y=value,col=variable)) +
labs(title="Average gas price with second differencing.",
y="Average Price",
color=NULL) + # title
scale_x_date(labels = lbls, breaks =brks) + # change to monthly ticks and labels
scale_fill_brewer( palette = 3) +
theme(legend.position="top")+theme_gray()
acf1=ggAcf(df5_diff2$Hydrous.Ethanol,200)
acf2=ggAcf(df5_diff2$Regular.Gasoline,200)
acf3=ggAcf(df5_diff2$LPG,200)
acf4=ggAcf(df5_diff2$Natural.Gas,200)
acf5=ggAcf(df5_diff2$Diesel,200)
ggarrange(acf1, acf2,acf3,acf4,acf5,
ncol = 1, nrow = 5)
VAR:product price as exogenous variables
https://www.r-econometrics.com/timeseries/varintro/
# df5_diff$date = NULL
# df5_diff = df5_diff[complete.cases(df5_diff2),]
var.fit2 = VAR(df5_scaled[,c(1:5)], 5, type = "trend", ic = "AIC",lag.max=3,season=80)
summary(var.fit2)##
## VAR Estimation Results:
## =========================
## Endogenous variables: Hydrous.Ethanol, Regular.Gasoline, LPG, Natural.Gas, Diesel
## Deterministic variables: trend
## Sample size: 730
## Log Likelihood: 8374.04
## Roots of the characteristic polynomial:
## 1.001 0.9926 0.9753 0.966 0.9204 0.8477 0.4354 0.4305 0.4305 0.4093 0.4093 0.3389 0.1978 0.1978 0.1978
## Call:
## VAR(y = df5_scaled[, c(1:5)], p = 5, type = "trend", season = 80L,
## lag.max = 3, ic = "AIC")
##
##
## Estimation results for equation Hydrous.Ethanol:
## ================================================
## Hydrous.Ethanol = Hydrous.Ethanol.l1 + Regular.Gasoline.l1 + LPG.l1 + Natural.Gas.l1 + Diesel.l1 + Hydrous.Ethanol.l2 + Regular.Gasoline.l2 + LPG.l2 + Natural.Gas.l2 + Diesel.l2 + Hydrous.Ethanol.l3 + Regular.Gasoline.l3 + LPG.l3 + Natural.Gas.l3 + Diesel.l3 + trend + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 + sd7 + sd8 + sd9 + sd10 + sd11 + sd12 + sd13 + sd14 + sd15 + sd16 + sd17 + sd18 + sd19 + sd20 + sd21 + sd22 + sd23 + sd24 + sd25 + sd26 + sd27 + sd28 + sd29 + sd30 + sd31 + sd32 + sd33 + sd34 + sd35 + sd36 + sd37 + sd38 + sd39 + sd40 + sd41 + sd42 + sd43 + sd44 + sd45 + sd46 + sd47 + sd48 + sd49 + sd50 + sd51 + sd52 + sd53 + sd54 + sd55 + sd56 + sd57 + sd58 + sd59 + sd60 + sd61 + sd62 + sd63 + sd64 + sd65 + sd66 + sd67 + sd68 + sd69 + sd70 + sd71 + sd72 + sd73 + sd74 + sd75 + sd76 + sd77 + sd78 + sd79
##
## Estimate Std. Error t value Pr(>|t|)
## Hydrous.Ethanol.l1 1.488e+00 4.915e-02 30.265 < 2e-16 ***
## Regular.Gasoline.l1 -1.536e-01 4.503e-02 -3.411 0.000688 ***
## LPG.l1 -3.950e-02 4.200e-02 -0.940 0.347421
## Natural.Gas.l1 1.339e-02 2.435e-02 0.550 0.582686
## Diesel.l1 4.145e-02 3.566e-02 1.162 0.245515
## Hydrous.Ethanol.l2 -2.027e-01 8.769e-02 -2.311 0.021137 *
## Regular.Gasoline.l2 -2.199e-02 7.187e-02 -0.306 0.759725
## LPG.l2 1.202e-01 6.569e-02 1.829 0.067840 .
## Natural.Gas.l2 -1.707e-02 2.333e-02 -0.732 0.464481
## Diesel.l2 3.740e-02 5.508e-02 0.679 0.497340
## Hydrous.Ethanol.l3 -2.992e-01 4.899e-02 -6.107 1.77e-09 ***
## Regular.Gasoline.l3 1.593e-01 4.581e-02 3.476 0.000543 ***
## LPG.l3 -5.548e-02 4.269e-02 -1.300 0.194206
## Natural.Gas.l3 -6.289e-03 2.442e-02 -0.258 0.796849
## Diesel.l3 -6.424e-02 3.636e-02 -1.767 0.077755 .
## trend 5.371e-06 2.567e-06 2.093 0.036765 *
## sd1 -5.663e-03 1.098e-02 -0.516 0.606123
## sd2 -4.813e-03 1.098e-02 -0.438 0.661180
## sd3 4.617e-03 1.097e-02 0.421 0.674011
## sd4 -4.662e-03 1.070e-02 -0.436 0.663152
## sd5 2.378e-03 1.069e-02 0.222 0.824102
## sd6 3.366e-03 1.068e-02 0.315 0.752806
## sd7 -1.871e-03 1.071e-02 -0.175 0.861370
## sd8 -3.748e-03 1.069e-02 -0.350 0.726129
## sd9 -3.725e-03 1.070e-02 -0.348 0.727833
## sd10 -2.112e-03 1.073e-02 -0.197 0.844023
## sd11 1.195e-03 1.088e-02 0.110 0.912583
## sd12 1.115e-02 1.086e-02 1.027 0.304978
## sd13 -2.605e-03 1.071e-02 -0.243 0.807878
## sd14 1.349e-02 1.098e-02 1.229 0.219580
## sd15 -5.156e-03 1.099e-02 -0.469 0.639168
## sd16 4.701e-03 1.099e-02 0.428 0.668869
## sd17 -5.005e-03 1.100e-02 -0.455 0.649222
## sd18 -6.416e-03 1.096e-02 -0.585 0.558554
## sd19 -1.223e-03 1.099e-02 -0.111 0.911404
## sd20 -1.983e-03 1.098e-02 -0.181 0.856785
## sd21 -5.403e-03 1.096e-02 -0.493 0.622285
## sd22 1.762e-03 1.096e-02 0.161 0.872287
## sd23 -6.670e-03 1.098e-02 -0.607 0.543822
## sd24 2.742e-03 1.096e-02 0.250 0.802603
## sd25 -6.411e-03 1.096e-02 -0.585 0.558930
## sd26 -1.020e-02 1.098e-02 -0.929 0.353290
## sd27 1.129e-02 1.100e-02 1.026 0.305085
## sd28 4.002e-05 1.119e-02 0.004 0.997146
## sd29 1.891e-03 1.119e-02 0.169 0.865811
## sd30 5.753e-04 1.106e-02 0.052 0.958531
## sd31 1.245e-02 1.102e-02 1.130 0.258864
## sd32 -3.370e-05 1.102e-02 -0.003 0.997560
## sd33 -4.496e-03 1.100e-02 -0.409 0.682781
## sd34 -9.581e-04 1.098e-02 -0.087 0.930504
## sd35 8.667e-03 1.097e-02 0.790 0.429689
## sd36 9.560e-03 1.102e-02 0.868 0.385881
## sd37 9.529e-03 1.102e-02 0.865 0.387584
## sd38 -1.586e-02 1.101e-02 -1.441 0.150154
## sd39 1.250e-02 1.104e-02 1.132 0.257929
## sd40 -1.931e-03 1.102e-02 -0.175 0.860971
## sd41 -1.569e-02 1.099e-02 -1.428 0.153857
## sd42 -4.275e-03 1.101e-02 -0.388 0.697936
## sd43 -2.027e-02 1.101e-02 -1.841 0.066056 .
## sd44 -6.159e-03 1.099e-02 -0.560 0.575478
## sd45 2.550e-02 1.101e-02 2.316 0.020894 *
## sd46 -6.180e-04 1.113e-02 -0.056 0.955727
## sd47 2.287e-03 1.105e-02 0.207 0.836185
## sd48 -1.901e-03 1.100e-02 -0.173 0.862865
## sd49 -1.346e-03 1.104e-02 -0.122 0.903038
## sd50 5.245e-03 1.099e-02 0.477 0.633270
## sd51 -5.579e-04 1.098e-02 -0.051 0.959503
## sd52 7.407e-03 1.098e-02 0.675 0.500180
## sd53 8.370e-03 1.099e-02 0.762 0.446465
## sd54 -1.780e-03 1.102e-02 -0.162 0.871663
## sd55 -1.053e-03 1.099e-02 -0.096 0.923721
## sd56 1.254e-02 1.100e-02 1.139 0.254934
## sd57 -2.833e-03 1.101e-02 -0.257 0.797009
## sd58 -4.333e-03 1.102e-02 -0.393 0.694255
## sd59 -1.746e-02 1.105e-02 -1.580 0.114567
## sd60 -7.120e-04 1.101e-02 -0.065 0.948464
## sd61 -1.207e-02 1.101e-02 -1.097 0.273250
## sd62 -3.289e-03 1.100e-02 -0.299 0.765034
## sd63 -6.604e-03 1.099e-02 -0.601 0.548122
## sd64 -1.761e-04 1.101e-02 -0.016 0.987235
## sd65 -8.652e-03 1.099e-02 -0.787 0.431329
## sd66 3.965e-03 1.098e-02 0.361 0.718198
## sd67 -5.637e-03 1.100e-02 -0.513 0.608464
## sd68 4.250e-03 1.097e-02 0.387 0.698698
## sd69 5.732e-03 1.099e-02 0.521 0.602312
## sd70 -7.180e-04 1.101e-02 -0.065 0.948015
## sd71 -2.529e-03 1.099e-02 -0.230 0.818150
## sd72 4.461e-04 1.097e-02 0.041 0.967578
## sd73 9.124e-03 1.096e-02 0.832 0.405462
## sd74 -1.113e-02 1.097e-02 -1.015 0.310647
## sd75 -9.452e-03 1.098e-02 -0.861 0.389551
## sd76 -2.183e-03 1.096e-02 -0.199 0.842192
## sd77 5.641e-03 1.096e-02 0.515 0.607062
## sd78 2.494e-03 1.104e-02 0.226 0.821289
## sd79 -2.980e-03 1.099e-02 -0.271 0.786369
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.0232 on 635 degrees of freedom
## Multiple R-Squared: 0.9994, Adjusted R-squared: 0.9993
## F-statistic: 1.161e+04 on 95 and 635 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation Regular.Gasoline:
## =================================================
## Regular.Gasoline = Hydrous.Ethanol.l1 + Regular.Gasoline.l1 + LPG.l1 + Natural.Gas.l1 + Diesel.l1 + Hydrous.Ethanol.l2 + Regular.Gasoline.l2 + LPG.l2 + Natural.Gas.l2 + Diesel.l2 + Hydrous.Ethanol.l3 + Regular.Gasoline.l3 + LPG.l3 + Natural.Gas.l3 + Diesel.l3 + trend + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 + sd7 + sd8 + sd9 + sd10 + sd11 + sd12 + sd13 + sd14 + sd15 + sd16 + sd17 + sd18 + sd19 + sd20 + sd21 + sd22 + sd23 + sd24 + sd25 + sd26 + sd27 + sd28 + sd29 + sd30 + sd31 + sd32 + sd33 + sd34 + sd35 + sd36 + sd37 + sd38 + sd39 + sd40 + sd41 + sd42 + sd43 + sd44 + sd45 + sd46 + sd47 + sd48 + sd49 + sd50 + sd51 + sd52 + sd53 + sd54 + sd55 + sd56 + sd57 + sd58 + sd59 + sd60 + sd61 + sd62 + sd63 + sd64 + sd65 + sd66 + sd67 + sd68 + sd69 + sd70 + sd71 + sd72 + sd73 + sd74 + sd75 + sd76 + sd77 + sd78 + sd79
##
## Estimate Std. Error t value Pr(>|t|)
## Hydrous.Ethanol.l1 7.966e-02 6.865e-02 1.160 0.24635
## Regular.Gasoline.l1 1.090e+00 6.289e-02 17.329 < 2e-16 ***
## LPG.l1 -3.613e-02 5.867e-02 -0.616 0.53817
## Natural.Gas.l1 8.789e-02 3.400e-02 2.585 0.00997 **
## Diesel.l1 1.156e-01 4.980e-02 2.321 0.02061 *
## Hydrous.Ethanol.l2 2.111e-02 1.225e-01 0.172 0.86319
## Regular.Gasoline.l2 -2.245e-01 1.004e-01 -2.237 0.02564 *
## LPG.l2 6.516e-02 9.174e-02 0.710 0.47779
## Natural.Gas.l2 -1.063e-01 3.258e-02 -3.261 0.00117 **
## Diesel.l2 -6.657e-02 7.693e-02 -0.865 0.38719
## Hydrous.Ethanol.l3 -1.060e-01 6.842e-02 -1.549 0.12181
## Regular.Gasoline.l3 9.455e-02 6.399e-02 1.478 0.13999
## LPG.l3 9.419e-03 5.963e-02 0.158 0.87454
## Natural.Gas.l3 1.579e-03 3.410e-02 0.046 0.96308
## Diesel.l3 -2.651e-02 5.078e-02 -0.522 0.60183
## trend 7.282e-06 3.585e-06 2.031 0.04262 *
## sd1 -3.700e-03 1.533e-02 -0.241 0.80939
## sd2 -5.974e-03 1.533e-02 -0.390 0.69691
## sd3 6.110e-04 1.532e-02 0.040 0.96820
## sd4 -4.534e-03 1.494e-02 -0.303 0.76167
## sd5 -2.712e-03 1.494e-02 -0.182 0.85598
## sd6 -7.188e-04 1.492e-02 -0.048 0.96159
## sd7 6.621e-03 1.496e-02 0.443 0.65817
## sd8 7.235e-03 1.494e-02 0.484 0.62830
## sd9 7.858e-03 1.494e-02 0.526 0.59915
## sd10 -9.638e-03 1.499e-02 -0.643 0.52042
## sd11 -3.658e-03 1.520e-02 -0.241 0.80985
## sd12 5.087e-03 1.517e-02 0.335 0.73756
## sd13 -2.969e-04 1.495e-02 -0.020 0.98417
## sd14 2.455e-03 1.534e-02 0.160 0.87288
## sd15 -6.485e-03 1.535e-02 -0.422 0.67285
## sd16 1.017e-02 1.534e-02 0.663 0.50759
## sd17 -8.794e-03 1.536e-02 -0.572 0.56720
## sd18 -6.935e-03 1.531e-02 -0.453 0.65072
## sd19 3.134e-04 1.535e-02 0.020 0.98371
## sd20 -5.197e-03 1.534e-02 -0.339 0.73481
## sd21 -6.704e-03 1.531e-02 -0.438 0.66166
## sd22 -3.977e-04 1.530e-02 -0.026 0.97927
## sd23 -1.598e-03 1.534e-02 -0.104 0.91705
## sd24 1.465e-03 1.531e-02 0.096 0.92383
## sd25 -1.481e-02 1.531e-02 -0.967 0.33367
## sd26 -8.600e-03 1.533e-02 -0.561 0.57510
## sd27 2.187e-03 1.537e-02 0.142 0.88688
## sd28 -3.488e-03 1.562e-02 -0.223 0.82339
## sd29 -6.266e-03 1.562e-02 -0.401 0.68847
## sd30 1.279e-02 1.545e-02 0.828 0.40808
## sd31 1.664e-02 1.539e-02 1.082 0.27988
## sd32 -1.081e-02 1.539e-02 -0.703 0.48260
## sd33 -1.984e-03 1.536e-02 -0.129 0.89725
## sd34 -5.692e-03 1.534e-02 -0.371 0.71071
## sd35 -1.007e-02 1.532e-02 -0.658 0.51104
## sd36 7.943e-03 1.539e-02 0.516 0.60590
## sd37 1.039e-03 1.539e-02 0.067 0.94621
## sd38 -6.514e-03 1.538e-02 -0.424 0.67198
## sd39 6.357e-03 1.541e-02 0.412 0.68016
## sd40 -4.748e-03 1.539e-02 -0.308 0.75786
## sd41 -1.389e-02 1.535e-02 -0.905 0.36606
## sd42 -1.312e-03 1.538e-02 -0.085 0.93205
## sd43 -1.645e-02 1.537e-02 -1.070 0.28493
## sd44 -6.438e-03 1.535e-02 -0.419 0.67507
## sd45 4.856e-02 1.538e-02 3.157 0.00167 **
## sd46 -1.089e-02 1.554e-02 -0.701 0.48378
## sd47 -5.565e-03 1.544e-02 -0.360 0.71860
## sd48 -5.495e-03 1.536e-02 -0.358 0.72071
## sd49 8.408e-05 1.542e-02 0.005 0.99565
## sd50 -2.535e-03 1.535e-02 -0.165 0.86886
## sd51 9.752e-03 1.534e-02 0.636 0.52513
## sd52 -2.257e-03 1.533e-02 -0.147 0.88301
## sd53 2.285e-02 1.535e-02 1.489 0.13693
## sd54 -7.066e-03 1.539e-02 -0.459 0.64621
## sd55 -9.801e-03 1.536e-02 -0.638 0.52355
## sd56 4.402e-03 1.537e-02 0.286 0.77465
## sd57 -9.213e-03 1.538e-02 -0.599 0.54925
## sd58 -7.681e-03 1.539e-02 -0.499 0.61783
## sd59 -1.124e-02 1.543e-02 -0.729 0.46656
## sd60 5.410e-04 1.538e-02 0.035 0.97195
## sd61 -2.746e-03 1.538e-02 -0.179 0.85833
## sd62 3.031e-03 1.536e-02 0.197 0.84366
## sd63 -1.812e-03 1.535e-02 -0.118 0.90604
## sd64 -1.160e-03 1.537e-02 -0.075 0.93984
## sd65 -3.053e-03 1.535e-02 -0.199 0.84237
## sd66 -5.380e-05 1.534e-02 -0.004 0.99720
## sd67 -6.839e-03 1.536e-02 -0.445 0.65634
## sd68 5.547e-03 1.533e-02 0.362 0.71752
## sd69 2.647e-02 1.536e-02 1.724 0.08521 .
## sd70 -1.133e-02 1.537e-02 -0.737 0.46157
## sd71 -3.493e-03 1.535e-02 -0.227 0.82012
## sd72 1.415e-03 1.532e-02 0.092 0.92642
## sd73 -7.725e-03 1.531e-02 -0.505 0.61399
## sd74 -1.105e-02 1.533e-02 -0.721 0.47128
## sd75 -6.187e-03 1.533e-02 -0.404 0.68670
## sd76 -8.186e-03 1.531e-02 -0.535 0.59295
## sd77 3.395e-02 1.531e-02 2.217 0.02695 *
## sd78 -2.091e-03 1.541e-02 -0.136 0.89211
## sd79 -6.597e-03 1.535e-02 -0.430 0.66752
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.0324 on 635 degrees of freedom
## Multiple R-Squared: 0.9987, Adjusted R-squared: 0.9985
## F-statistic: 5037 on 95 and 635 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation LPG:
## ====================================
## LPG = Hydrous.Ethanol.l1 + Regular.Gasoline.l1 + LPG.l1 + Natural.Gas.l1 + Diesel.l1 + Hydrous.Ethanol.l2 + Regular.Gasoline.l2 + LPG.l2 + Natural.Gas.l2 + Diesel.l2 + Hydrous.Ethanol.l3 + Regular.Gasoline.l3 + LPG.l3 + Natural.Gas.l3 + Diesel.l3 + trend + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 + sd7 + sd8 + sd9 + sd10 + sd11 + sd12 + sd13 + sd14 + sd15 + sd16 + sd17 + sd18 + sd19 + sd20 + sd21 + sd22 + sd23 + sd24 + sd25 + sd26 + sd27 + sd28 + sd29 + sd30 + sd31 + sd32 + sd33 + sd34 + sd35 + sd36 + sd37 + sd38 + sd39 + sd40 + sd41 + sd42 + sd43 + sd44 + sd45 + sd46 + sd47 + sd48 + sd49 + sd50 + sd51 + sd52 + sd53 + sd54 + sd55 + sd56 + sd57 + sd58 + sd59 + sd60 + sd61 + sd62 + sd63 + sd64 + sd65 + sd66 + sd67 + sd68 + sd69 + sd70 + sd71 + sd72 + sd73 + sd74 + sd75 + sd76 + sd77 + sd78 + sd79
##
## Estimate Std. Error t value Pr(>|t|)
## Hydrous.Ethanol.l1 3.146e-02 4.630e-02 0.679 0.497152
## Regular.Gasoline.l1 -3.694e-02 4.242e-02 -0.871 0.384207
## LPG.l1 1.208e+00 3.957e-02 30.530 < 2e-16 ***
## Natural.Gas.l1 8.371e-04 2.293e-02 0.037 0.970895
## Diesel.l1 7.475e-02 3.359e-02 2.225 0.026413 *
## Hydrous.Ethanol.l2 -1.103e-01 8.260e-02 -1.336 0.182184
## Regular.Gasoline.l2 4.717e-02 6.770e-02 0.697 0.486165
## LPG.l2 -1.503e-01 6.188e-02 -2.429 0.015415 *
## Natural.Gas.l2 4.959e-02 2.197e-02 2.257 0.024347 *
## Diesel.l2 -5.493e-02 5.188e-02 -1.059 0.290125
## Hydrous.Ethanol.l3 7.062e-02 4.614e-02 1.530 0.126411
## Regular.Gasoline.l3 5.872e-04 4.316e-02 0.014 0.989148
## LPG.l3 -6.261e-02 4.021e-02 -1.557 0.120020
## Natural.Gas.l3 -5.203e-02 2.300e-02 -2.262 0.024044 *
## Diesel.l3 -1.430e-02 3.425e-02 -0.417 0.676561
## trend 9.235e-06 2.418e-06 3.820 0.000147 ***
## sd1 -2.264e-02 1.034e-02 -2.190 0.028911 *
## sd2 -9.164e-03 1.034e-02 -0.886 0.375792
## sd3 -1.412e-02 1.033e-02 -1.367 0.172211
## sd4 -1.231e-02 1.008e-02 -1.221 0.222381
## sd5 -9.225e-03 1.007e-02 -0.916 0.360142
## sd6 -1.710e-02 1.006e-02 -1.700 0.089675 .
## sd7 -1.482e-02 1.009e-02 -1.469 0.142265
## sd8 -1.102e-02 1.007e-02 -1.094 0.274438
## sd9 -6.120e-03 1.008e-02 -0.607 0.543899
## sd10 -1.702e-02 1.011e-02 -1.684 0.092661 .
## sd11 -1.053e-02 1.025e-02 -1.027 0.304592
## sd12 -1.516e-02 1.023e-02 -1.481 0.139115
## sd13 -1.463e-02 1.009e-02 -1.451 0.147361
## sd14 -1.169e-02 1.034e-02 -1.130 0.259032
## sd15 -1.011e-02 1.035e-02 -0.976 0.329399
## sd16 -1.326e-02 1.035e-02 -1.281 0.200573
## sd17 -1.354e-02 1.036e-02 -1.307 0.191625
## sd18 -1.372e-02 1.033e-02 -1.328 0.184501
## sd19 -1.657e-02 1.035e-02 -1.601 0.109954
## sd20 -9.620e-03 1.034e-02 -0.930 0.352739
## sd21 -1.408e-02 1.033e-02 -1.363 0.173212
## sd22 -1.433e-02 1.032e-02 -1.389 0.165417
## sd23 -1.581e-02 1.034e-02 -1.529 0.126807
## sd24 -1.059e-02 1.033e-02 -1.026 0.305469
## sd25 -1.568e-02 1.033e-02 -1.518 0.129449
## sd26 -8.989e-03 1.034e-02 -0.869 0.385068
## sd27 3.793e-02 1.036e-02 3.659 0.000274 ***
## sd28 -4.838e-03 1.054e-02 -0.459 0.646244
## sd29 -1.452e-02 1.054e-02 -1.378 0.168700
## sd30 -1.569e-02 1.042e-02 -1.506 0.132531
## sd31 -1.223e-02 1.038e-02 -1.179 0.239017
## sd32 -1.121e-02 1.038e-02 -1.080 0.280367
## sd33 -1.281e-02 1.036e-02 -1.236 0.216753
## sd34 -1.338e-02 1.034e-02 -1.293 0.196345
## sd35 -8.810e-03 1.033e-02 -0.853 0.394132
## sd36 -8.323e-03 1.038e-02 -0.802 0.422875
## sd37 -1.508e-02 1.038e-02 -1.452 0.146963
## sd38 -1.097e-02 1.037e-02 -1.058 0.290536
## sd39 -1.050e-02 1.039e-02 -1.010 0.312966
## sd40 -8.326e-03 1.038e-02 -0.802 0.422914
## sd41 -1.569e-02 1.035e-02 -1.516 0.130090
## sd42 -1.097e-02 1.037e-02 -1.058 0.290682
## sd43 -1.359e-02 1.037e-02 -1.311 0.190429
## sd44 -9.403e-03 1.035e-02 -0.908 0.364139
## sd45 -1.639e-02 1.037e-02 -1.580 0.114583
## sd46 -1.964e-02 1.048e-02 -1.874 0.061374 .
## sd47 -1.038e-02 1.041e-02 -0.996 0.319412
## sd48 -1.225e-02 1.036e-02 -1.182 0.237590
## sd49 -1.791e-02 1.040e-02 -1.722 0.085628 .
## sd50 -1.048e-02 1.035e-02 -1.013 0.311546
## sd51 -1.347e-02 1.034e-02 -1.302 0.193462
## sd52 1.314e-03 1.034e-02 0.127 0.898905
## sd53 -1.480e-02 1.035e-02 -1.430 0.153110
## sd54 4.667e-03 1.038e-02 0.450 0.653001
## sd55 -1.720e-02 1.036e-02 -1.661 0.097252 .
## sd56 -8.244e-03 1.037e-02 -0.795 0.426725
## sd57 9.739e-03 1.037e-02 0.939 0.348003
## sd58 -6.085e-03 1.038e-02 -0.586 0.557830
## sd59 -1.993e-02 1.041e-02 -1.914 0.056022 .
## sd60 -4.765e-03 1.037e-02 -0.459 0.646093
## sd61 -1.509e-02 1.037e-02 -1.455 0.146114
## sd62 -8.933e-03 1.036e-02 -0.862 0.388950
## sd63 -1.060e-02 1.035e-02 -1.023 0.306467
## sd64 -1.278e-02 1.037e-02 -1.233 0.218138
## sd65 -1.098e-02 1.035e-02 -1.061 0.289078
## sd66 -6.616e-03 1.034e-02 -0.640 0.522702
## sd67 -1.849e-02 1.036e-02 -1.785 0.074724 .
## sd68 -1.355e-02 1.034e-02 -1.310 0.190553
## sd69 -1.707e-02 1.036e-02 -1.648 0.099801 .
## sd70 -1.189e-02 1.037e-02 -1.147 0.251837
## sd71 -1.642e-02 1.036e-02 -1.586 0.113236
## sd72 -1.745e-02 1.033e-02 -1.689 0.091763 .
## sd73 -1.557e-02 1.032e-02 -1.508 0.131964
## sd74 -1.997e-02 1.034e-02 -1.932 0.053847 .
## sd75 -1.577e-02 1.034e-02 -1.525 0.127866
## sd76 -1.541e-02 1.032e-02 -1.493 0.135958
## sd77 -1.269e-02 1.033e-02 -1.229 0.219440
## sd78 -1.472e-02 1.039e-02 -1.416 0.157339
## sd79 -1.258e-02 1.035e-02 -1.215 0.224775
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.02185 on 635 degrees of freedom
## Multiple R-Squared: 0.9994, Adjusted R-squared: 0.9993
## F-statistic: 1.162e+04 on 95 and 635 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation Natural.Gas:
## ============================================
## Natural.Gas = Hydrous.Ethanol.l1 + Regular.Gasoline.l1 + LPG.l1 + Natural.Gas.l1 + Diesel.l1 + Hydrous.Ethanol.l2 + Regular.Gasoline.l2 + LPG.l2 + Natural.Gas.l2 + Diesel.l2 + Hydrous.Ethanol.l3 + Regular.Gasoline.l3 + LPG.l3 + Natural.Gas.l3 + Diesel.l3 + trend + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 + sd7 + sd8 + sd9 + sd10 + sd11 + sd12 + sd13 + sd14 + sd15 + sd16 + sd17 + sd18 + sd19 + sd20 + sd21 + sd22 + sd23 + sd24 + sd25 + sd26 + sd27 + sd28 + sd29 + sd30 + sd31 + sd32 + sd33 + sd34 + sd35 + sd36 + sd37 + sd38 + sd39 + sd40 + sd41 + sd42 + sd43 + sd44 + sd45 + sd46 + sd47 + sd48 + sd49 + sd50 + sd51 + sd52 + sd53 + sd54 + sd55 + sd56 + sd57 + sd58 + sd59 + sd60 + sd61 + sd62 + sd63 + sd64 + sd65 + sd66 + sd67 + sd68 + sd69 + sd70 + sd71 + sd72 + sd73 + sd74 + sd75 + sd76 + sd77 + sd78 + sd79
##
## Estimate Std. Error t value Pr(>|t|)
## Hydrous.Ethanol.l1 9.559e-03 7.947e-02 0.120 0.904290
## Regular.Gasoline.l1 5.462e-02 7.280e-02 0.750 0.453388
## LPG.l1 1.131e-01 6.791e-02 1.665 0.096441 .
## Natural.Gas.l1 3.559e-01 3.936e-02 9.041 < 2e-16 ***
## Diesel.l1 1.951e-02 5.765e-02 0.338 0.735190
## Hydrous.Ethanol.l2 -5.436e-03 1.418e-01 -0.038 0.969423
## Regular.Gasoline.l2 -1.207e-01 1.162e-01 -1.039 0.299342
## LPG.l2 -1.622e-01 1.062e-01 -1.527 0.127154
## Natural.Gas.l2 4.818e-01 3.771e-02 12.776 < 2e-16 ***
## Diesel.l2 1.684e-01 8.905e-02 1.891 0.059055 .
## Hydrous.Ethanol.l3 -1.137e-02 7.920e-02 -0.144 0.885850
## Regular.Gasoline.l3 6.973e-02 7.407e-02 0.941 0.346858
## LPG.l3 5.455e-02 6.902e-02 0.790 0.429635
## Natural.Gas.l3 1.346e-01 3.948e-02 3.408 0.000695 ***
## Diesel.l3 -1.648e-01 5.878e-02 -2.803 0.005223 **
## trend 1.622e-05 4.149e-06 3.909 0.000103 ***
## sd1 -1.305e-02 1.775e-02 -0.735 0.462333
## sd2 -2.275e-02 1.774e-02 -1.282 0.200272
## sd3 -1.798e-02 1.774e-02 -1.014 0.311000
## sd4 -1.776e-02 1.730e-02 -1.027 0.304944
## sd5 1.250e-02 1.729e-02 0.723 0.469943
## sd6 -9.481e-03 1.727e-02 -0.549 0.583187
## sd7 -9.261e-03 1.731e-02 -0.535 0.592910
## sd8 -9.678e-03 1.729e-02 -0.560 0.575867
## sd9 -1.679e-02 1.730e-02 -0.971 0.331997
## sd10 -9.205e-03 1.735e-02 -0.531 0.595892
## sd11 -1.927e-02 1.759e-02 -1.096 0.273640
## sd12 7.343e-03 1.756e-02 0.418 0.676046
## sd13 -1.225e-02 1.731e-02 -0.708 0.479404
## sd14 -6.954e-03 1.775e-02 -0.392 0.695394
## sd15 -1.480e-02 1.777e-02 -0.833 0.405358
## sd16 -2.243e-02 1.776e-02 -1.263 0.207143
## sd17 -5.853e-03 1.778e-02 -0.329 0.742138
## sd18 -2.830e-02 1.772e-02 -1.597 0.110754
## sd19 -1.816e-02 1.777e-02 -1.022 0.307011
## sd20 -1.016e-02 1.775e-02 -0.572 0.567373
## sd21 6.967e-04 1.772e-02 0.039 0.968655
## sd22 -1.283e-02 1.771e-02 -0.724 0.469102
## sd23 -3.863e-03 1.775e-02 -0.218 0.827818
## sd24 2.138e-03 1.773e-02 0.121 0.904022
## sd25 -1.755e-02 1.772e-02 -0.990 0.322521
## sd26 -3.039e-02 1.775e-02 -1.712 0.087378 .
## sd27 -1.405e-03 1.779e-02 -0.079 0.937080
## sd28 1.253e-03 1.808e-02 0.069 0.944773
## sd29 -3.010e-02 1.808e-02 -1.664 0.096530 .
## sd30 -9.428e-03 1.788e-02 -0.527 0.598149
## sd31 8.248e-03 1.781e-02 0.463 0.643533
## sd32 -8.909e-03 1.781e-02 -0.500 0.617135
## sd33 -1.503e-02 1.778e-02 -0.846 0.398044
## sd34 1.765e-02 1.775e-02 0.994 0.320615
## sd35 -1.180e-02 1.773e-02 -0.665 0.506001
## sd36 -1.195e-02 1.781e-02 -0.671 0.502544
## sd37 2.442e-03 1.782e-02 0.137 0.891016
## sd38 -1.969e-02 1.780e-02 -1.106 0.269042
## sd39 -1.190e-02 1.784e-02 -0.667 0.505111
## sd40 1.691e-02 1.782e-02 0.949 0.342846
## sd41 -1.316e-02 1.777e-02 -0.741 0.459196
## sd42 -1.816e-02 1.780e-02 -1.020 0.307883
## sd43 4.130e-03 1.779e-02 0.232 0.816547
## sd44 8.353e-03 1.777e-02 0.470 0.638467
## sd45 4.277e-03 1.780e-02 0.240 0.810254
## sd46 -1.702e-02 1.799e-02 -0.946 0.344320
## sd47 3.647e-04 1.787e-02 0.020 0.983722
## sd48 3.180e-03 1.779e-02 0.179 0.858134
## sd49 -2.592e-02 1.785e-02 -1.452 0.146997
## sd50 -2.233e-02 1.776e-02 -1.257 0.209259
## sd51 -8.026e-03 1.775e-02 -0.452 0.651380
## sd52 -2.453e-03 1.775e-02 -0.138 0.890117
## sd53 -4.399e-03 1.776e-02 -0.248 0.804476
## sd54 1.984e-03 1.781e-02 0.111 0.911327
## sd55 -1.640e-02 1.777e-02 -0.923 0.356593
## sd56 -1.797e-02 1.779e-02 -1.010 0.312921
## sd57 -5.023e-03 1.780e-02 -0.282 0.777855
## sd58 -2.103e-02 1.781e-02 -1.181 0.238116
## sd59 -1.583e-02 1.786e-02 -0.886 0.376001
## sd60 -2.031e-02 1.780e-02 -1.141 0.254375
## sd61 -1.577e-02 1.780e-02 -0.886 0.375986
## sd62 2.951e-03 1.778e-02 0.166 0.868234
## sd63 -2.118e-02 1.777e-02 -1.192 0.233774
## sd64 -8.171e-03 1.779e-02 -0.459 0.646196
## sd65 -1.067e-02 1.776e-02 -0.601 0.548206
## sd66 -1.647e-02 1.775e-02 -0.927 0.354078
## sd67 -1.181e-02 1.778e-02 -0.664 0.506972
## sd68 -1.741e-02 1.774e-02 -0.981 0.326767
## sd69 4.657e-03 1.777e-02 0.262 0.793404
## sd70 -3.677e-03 1.780e-02 -0.207 0.836348
## sd71 -2.079e-02 1.777e-02 -1.170 0.242597
## sd72 -8.160e-03 1.774e-02 -0.460 0.645597
## sd73 -1.023e-02 1.772e-02 -0.578 0.563792
## sd74 -1.166e-02 1.774e-02 -0.658 0.511051
## sd75 9.967e-03 1.775e-02 0.562 0.574601
## sd76 -2.916e-03 1.772e-02 -0.165 0.869294
## sd77 -4.422e-03 1.772e-02 -0.249 0.803070
## sd78 -1.433e-02 1.784e-02 -0.803 0.422043
## sd79 5.217e-03 1.777e-02 0.294 0.769155
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.03751 on 635 degrees of freedom
## Multiple R-Squared: 0.9981, Adjusted R-squared: 0.9978
## F-statistic: 3541 on 95 and 635 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation Diesel:
## =======================================
## Diesel = Hydrous.Ethanol.l1 + Regular.Gasoline.l1 + LPG.l1 + Natural.Gas.l1 + Diesel.l1 + Hydrous.Ethanol.l2 + Regular.Gasoline.l2 + LPG.l2 + Natural.Gas.l2 + Diesel.l2 + Hydrous.Ethanol.l3 + Regular.Gasoline.l3 + LPG.l3 + Natural.Gas.l3 + Diesel.l3 + trend + sd1 + sd2 + sd3 + sd4 + sd5 + sd6 + sd7 + sd8 + sd9 + sd10 + sd11 + sd12 + sd13 + sd14 + sd15 + sd16 + sd17 + sd18 + sd19 + sd20 + sd21 + sd22 + sd23 + sd24 + sd25 + sd26 + sd27 + sd28 + sd29 + sd30 + sd31 + sd32 + sd33 + sd34 + sd35 + sd36 + sd37 + sd38 + sd39 + sd40 + sd41 + sd42 + sd43 + sd44 + sd45 + sd46 + sd47 + sd48 + sd49 + sd50 + sd51 + sd52 + sd53 + sd54 + sd55 + sd56 + sd57 + sd58 + sd59 + sd60 + sd61 + sd62 + sd63 + sd64 + sd65 + sd66 + sd67 + sd68 + sd69 + sd70 + sd71 + sd72 + sd73 + sd74 + sd75 + sd76 + sd77 + sd78 + sd79
##
## Estimate Std. Error t value Pr(>|t|)
## Hydrous.Ethanol.l1 -1.768e-02 7.096e-02 -0.249 0.803291
## Regular.Gasoline.l1 -1.160e-01 6.501e-02 -1.785 0.074782 .
## LPG.l1 -1.344e-01 6.063e-02 -2.217 0.026982 *
## Natural.Gas.l1 1.110e-01 3.515e-02 3.159 0.001656 **
## Diesel.l1 1.278e+00 5.148e-02 24.824 < 2e-16 ***
## Hydrous.Ethanol.l2 1.585e-01 1.266e-01 1.252 0.211137
## Regular.Gasoline.l2 -4.529e-02 1.037e-01 -0.437 0.662573
## LPG.l2 2.092e-01 9.482e-02 2.206 0.027746 *
## Natural.Gas.l2 -1.265e-01 3.367e-02 -3.756 0.000189 ***
## Diesel.l2 -3.459e-01 7.951e-02 -4.351 1.58e-05 ***
## Hydrous.Ethanol.l3 -1.414e-01 7.071e-02 -1.999 0.046039 *
## Regular.Gasoline.l3 1.345e-01 6.614e-02 2.033 0.042466 *
## LPG.l3 -4.554e-02 6.163e-02 -0.739 0.460248
## Natural.Gas.l3 7.090e-03 3.525e-02 0.201 0.840662
## Diesel.l3 7.250e-02 5.249e-02 1.381 0.167718
## trend 1.031e-05 3.705e-06 2.783 0.005553 **
## sd1 7.351e-03 1.585e-02 0.464 0.642898
## sd2 -1.511e-03 1.584e-02 -0.095 0.924056
## sd3 1.005e-02 1.584e-02 0.635 0.525905
## sd4 1.262e-03 1.544e-02 0.082 0.934890
## sd5 3.784e-03 1.544e-02 0.245 0.806454
## sd6 7.538e-03 1.542e-02 0.489 0.625102
## sd7 1.839e-02 1.546e-02 1.190 0.234607
## sd8 2.543e-02 1.544e-02 1.647 0.100077
## sd9 1.478e-03 1.544e-02 0.096 0.923798
## sd10 -5.091e-02 1.549e-02 -3.286 0.001071 **
## sd11 3.333e-03 1.571e-02 0.212 0.831995
## sd12 -2.821e-03 1.568e-02 -0.180 0.857308
## sd13 2.538e-03 1.546e-02 0.164 0.869619
## sd14 1.793e-03 1.585e-02 0.113 0.909993
## sd15 2.606e-03 1.587e-02 0.164 0.869571
## sd16 1.911e-02 1.586e-02 1.205 0.228694
## sd17 4.005e-03 1.588e-02 0.252 0.800911
## sd18 3.669e-03 1.582e-02 0.232 0.816715
## sd19 2.771e-03 1.586e-02 0.175 0.861383
## sd20 -1.467e-03 1.585e-02 -0.093 0.926318
## sd21 1.350e-03 1.583e-02 0.085 0.932058
## sd22 -2.432e-03 1.582e-02 -0.154 0.877863
## sd23 2.044e-03 1.585e-02 0.129 0.897454
## sd24 1.278e-02 1.583e-02 0.808 0.419608
## sd25 -9.085e-03 1.583e-02 -0.574 0.566128
## sd26 -3.989e-03 1.585e-02 -0.252 0.801347
## sd27 -4.433e-04 1.588e-02 -0.028 0.977745
## sd28 3.970e-03 1.615e-02 0.246 0.805866
## sd29 -1.519e-03 1.615e-02 -0.094 0.925087
## sd30 2.298e-02 1.596e-02 1.440 0.150477
## sd31 1.064e-02 1.591e-02 0.669 0.503738
## sd32 -1.145e-03 1.590e-02 -0.072 0.942616
## sd33 4.608e-03 1.587e-02 0.290 0.771672
## sd34 -2.307e-03 1.585e-02 -0.146 0.884352
## sd35 -3.067e-03 1.583e-02 -0.194 0.846459
## sd36 6.243e-03 1.590e-02 0.393 0.694799
## sd37 -4.035e-04 1.591e-02 -0.025 0.979773
## sd38 -3.470e-03 1.589e-02 -0.218 0.827207
## sd39 -6.865e-04 1.593e-02 -0.043 0.965640
## sd40 -9.279e-04 1.591e-02 -0.058 0.953511
## sd41 -8.018e-03 1.587e-02 -0.505 0.613512
## sd42 -2.153e-03 1.589e-02 -0.135 0.892296
## sd43 -1.706e-03 1.589e-02 -0.107 0.914534
## sd44 -4.851e-03 1.587e-02 -0.306 0.759923
## sd45 2.391e-02 1.590e-02 1.504 0.133031
## sd46 5.480e-03 1.606e-02 0.341 0.733090
## sd47 3.628e-02 1.596e-02 2.274 0.023315 *
## sd48 -6.487e-03 1.588e-02 -0.408 0.683063
## sd49 4.568e-03 1.594e-02 0.287 0.774513
## sd50 1.987e-03 1.586e-02 0.125 0.900323
## sd51 1.079e-02 1.585e-02 0.681 0.496198
## sd52 1.087e-03 1.585e-02 0.069 0.945357
## sd53 2.814e-02 1.586e-02 1.774 0.076461 .
## sd54 -2.779e-03 1.590e-02 -0.175 0.861304
## sd55 1.036e-02 1.587e-02 0.652 0.514340
## sd56 6.323e-03 1.588e-02 0.398 0.690728
## sd57 2.398e-03 1.589e-02 0.151 0.880109
## sd58 8.310e-03 1.590e-02 0.523 0.601468
## sd59 2.834e-03 1.595e-02 0.178 0.859031
## sd60 -3.013e-03 1.590e-02 -0.190 0.849725
## sd61 9.425e-03 1.589e-02 0.593 0.553400
## sd62 1.421e-04 1.588e-02 0.009 0.992861
## sd63 5.417e-03 1.586e-02 0.341 0.732873
## sd64 5.031e-04 1.589e-02 0.032 0.974747
## sd65 1.356e-02 1.586e-02 0.855 0.392844
## sd66 2.524e-03 1.585e-02 0.159 0.873545
## sd67 3.391e-03 1.588e-02 0.214 0.830921
## sd68 3.356e-03 1.584e-02 0.212 0.832292
## sd69 3.295e-02 1.587e-02 2.076 0.038278 *
## sd70 6.419e-04 1.589e-02 0.040 0.967790
## sd71 4.090e-03 1.587e-02 0.258 0.796696
## sd72 3.771e-03 1.584e-02 0.238 0.811851
## sd73 5.206e-04 1.582e-02 0.033 0.973761
## sd74 -2.507e-04 1.584e-02 -0.016 0.987379
## sd75 -2.792e-03 1.585e-02 -0.176 0.860192
## sd76 -2.264e-03 1.582e-02 -0.143 0.886235
## sd77 2.242e-02 1.583e-02 1.417 0.156978
## sd78 5.506e-03 1.593e-02 0.346 0.729736
## sd79 9.216e-03 1.587e-02 0.581 0.561587
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.03349 on 635 degrees of freedom
## Multiple R-Squared: 0.9987, Adjusted R-squared: 0.9985
## F-statistic: 5219 on 95 and 635 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## Hydrous.Ethanol Regular.Gasoline LPG Natural.Gas
## Hydrous.Ethanol 5.382e-04 4.612e-04 1.958e-05 1.525e-05
## Regular.Gasoline 4.612e-04 1.050e-03 6.333e-05 8.447e-05
## LPG 1.958e-05 6.333e-05 4.776e-04 5.707e-05
## Natural.Gas 1.525e-05 8.447e-05 5.707e-05 1.407e-03
## Diesel 2.244e-04 6.910e-04 3.696e-05 5.607e-06
## Diesel
## Hydrous.Ethanol 2.244e-04
## Regular.Gasoline 6.910e-04
## LPG 3.696e-05
## Natural.Gas 5.607e-06
## Diesel 1.122e-03
##
## Correlation matrix of residuals:
## Hydrous.Ethanol Regular.Gasoline LPG Natural.Gas
## Hydrous.Ethanol 1.00000 0.61352 0.03863 0.017529
## Regular.Gasoline 0.61352 1.00000 0.08944 0.069508
## LPG 0.03863 0.08944 1.00000 0.069634
## Natural.Gas 0.01753 0.06951 0.06963 1.000000
## Diesel 0.28876 0.63674 0.05050 0.004464
## Diesel
## Hydrous.Ethanol 0.288760
## Regular.Gasoline 0.636744
## LPG 0.050499
## Natural.Gas 0.004464
## Diesel 1.000000#plot(var.fit)
pred_VAR2 <- predict(var.fit2,df5_scaled2[,c(1:5)],n.ahead=52)
#plot(pred_VAR2)
# compute the acf resduals
acf1=ggAcf(residuals(var.fit2)[,1],200)
acf2=ggAcf(residuals(var.fit2)[,2],200)
acf3=ggAcf(residuals(var.fit2)[,3],200)
acf4=ggAcf(residuals(var.fit2)[,4],200)
acf5=ggAcf(residuals(var.fit2)[,5],200)
ggarrange(acf1, acf2,acf3,acf4,acf5,
ncol = 1, nrow = 5)
for (i in 1:5){
check_r=checkresiduals(residuals(var.fit2)[,i])
}
# > names(var.fit2$varresult)
# [1] "Hydrous.Ethanol"
# [2] "Regular.Gasoline"
# [3] "LPG"
# [4] "Natural.Gas"
# [5] "Diesel"
for (i in 1:5){
print(Box.test(residuals(var.fit2)[,i], type = "Ljung-Box"))}##
## Box-Ljung test
##
## data: residuals(var.fit2)[, i]
## X-squared = 0.1318, df = 1, p-value = 0.7166
##
##
## Box-Ljung test
##
## data: residuals(var.fit2)[, i]
## X-squared = 0.0013848, df = 1, p-value = 0.9703
##
##
## Box-Ljung test
##
## data: residuals(var.fit2)[, i]
## X-squared = 0.015084, df = 1, p-value = 0.9023
##
##
## Box-Ljung test
##
## data: residuals(var.fit2)[, i]
## X-squared = 0.9275, df = 1, p-value = 0.3355
##
##
## Box-Ljung test
##
## data: residuals(var.fit2)[, i]
## X-squared = 0.00098154, df = 1, p-value = 0.975#pred_VAR2$fcst
#df_undiff1 = data.frame(num = 1:52)
# add_trend = function(num,name){
# df_undiff = data.frame(idx = 1:52)
# for (i in name){
# df_undiff[i] = df5[735,i]+cumsum(pred_VAR2$fcst[[i]][,num])}
# return(df_undiff)
# }
# undiff_avg = add_trend(1,name)
# undiff_lower = add_trend(2,name)
# undiff_upper = add_trend(3,name)
# data.frame( apply(df4[,2:6],2,scale))
# nor = function(v1){scales::rescale(v1, to=c(mean(v1)-0.5,max(v1)+0.5))}
# undiff_lower = data.frame( apply(undiff_lower[,2:6],2,nor))
# undiff_upper = data.frame( apply(undiff_upper[,2:6],2,nor))
#df_undiff1 = data.frame(num = 1:52)
# df_undiff1["Hydrous.Ethanol"] = df5$Hydrous.Ethanol[735]+cumsum(pred_VAR2$fcst[["Hydrous.Ethanol"]][,1])
# df_undiff1["Regular.Gasoline"] = df5$Hydrous.Ethanol[735]+cumsum(pred_VAR2$fcst[["Regular.Gasoline"]][,1])
# df_undiff1["Natural.Gas"] = df5$Hydrous.Ethanol[735]+cumsum(pred_VAR2$fcst[["Natural.Gas"]][,1])
# df_undiff1["LPG"] = df5$Hydrous.Ethanol[735]+cumsum(pred_VAR2$fcst[["LPG"]][,1])
# df_undiff1["Diesel"] = df5$Hydrous.Ethanol[735]+cumsum(pred_VAR2$fcst[["Diesel"]][,1])Computing the metrics and ploting the result
col_prod2 = brewer.pal(12,"Paired")
name = c("Hydrous.Ethanol","Regular.Gasoline","Natural.Gas","LPG","Diesel")
plot_result = function(pred.var,i,c1,c2){
df_plotpred = data.frame(date=as.Date(df5$date),value = c(rep(NA,733),pred_VAR2$fcst[[i]][,1]))
df_plotpred['lower'] = c(rep(NA,733),pred_VAR2$fcst[[i]][,2])
df_plotpred['upper'] = c(rep(NA,733),pred_VAR2$fcst[[i]][,3])
vis = ggplot() +
geom_line(data = df5,aes(date, Hydrous.Ethanol),col=col_prod2[c1]) +
geom_line(data=df_plotpred,aes(date, value),col=col_prod2[c2])+
geom_ribbon(data = df_plotpred,aes(x = date, ymax = upper, ymin = lower), alpha = 0.5, fill = col_prod2[c2])+rremove('xlab')+ theme_gray()
return(vis)
}
vis1_fit = plot_result(pred_VAR2,name[1],2,1)
vis2_fit = plot_result(pred_VAR2,name[2],4,3)
vis3_fit = plot_result(pred_VAR2,name[3],6,5)
vis4_fit = plot_result(pred_VAR2,name[4],8,7)
vis5_fit = plot_result(pred_VAR2,name[5],10,9)
ggarrange(vis1_fit, vis2_fit,vis3_fit,vis4_fit,vis5_fit, labels = c("Hydrous Ethanol", "Regular Gasoline","LPG","Natural Gas","Diesel"), ncol = 3, nrow = 2, font.label = list(size = 10, face = "bold"))
#c("Hydrous.Ethanol","Hydrous.Ethanol","Regular.Gasoline","Regular.Gasoline","Natural.Gas","Natural.Gas","LPG","LPG","Diesel","Diesel")
# reording the
df_acc_produc2t= data.frame(product=c(rep(NA,10)),err_type=c(rep(NA,10)),ME=c(rep(NA,10)),RMSE=c(rep(NA,10)),MAE=c(rep(NA,10)),MPE=c(rep(NA,10)),MAPE=c(rep(NA,10)))
for (i in 1:5) {
df_acc_produc2t[i,]=c(name[i],"train",accuracy(var.fit2$varresult[[i]])[1:5])
df_acc_produc2t[i+5,]=c(name[i],"test",accuracy(pred_VAR2$fcst[[i]][,"fcst"],df5_scaled2[,c(1:5)][,i]))
}
#df_acc_produc2t
#write.csv(df_acc_product,"df_acc_product.csv" )
# ggplot(data=df_acc_product)+
# geom_point(aes(product, RMSE))
df_acc_produc2t[,-c(1,2)] <- sapply(df_acc_produc2t[,-c(1,2)],as.numeric)
print(df_acc_produc2t, digits = 4)## product err_type ME RMSE MAE MPE MAPE
## 1 Hydrous.Ethanol train -1.274e-04 0.02164 0.014323 8.8169 15.336
## 2 Regular.Gasoline train 7.453e-05 0.03022 0.015172 1.0028 4.285
## 3 Natural.Gas train -8.667e-05 0.02038 0.009103 1.6804 4.020
## 4 LPG train -1.631e-04 0.03498 0.025236 3.0698 13.830
## 5 Diesel train -2.297e-05 0.03123 0.014716 0.5033 2.928
## 6 Hydrous.Ethanol test -4.647e-01 0.53156 0.466161 -25.1495 25.225
## 7 Regular.Gasoline test -1.991e-01 0.39598 0.332034 -10.4395 15.447
## 8 Natural.Gas test -3.780e-01 0.42877 0.377999 -17.0151 17.015
## 9 LPG test 4.850e-01 0.52692 0.484975 19.3837 19.384
## 10 Diesel test 8.067e-02 0.19910 0.133131 3.4072 6.190#read.csv("df_acc_product.csv" )VAR: price info as exogenous variables
# function for extract the data
#colnames(df4) = c('start_date',"Hydrous Ethanol", "Regular Gasoline", "LPG","Natural Gas","Diesel" )
# which(df4$start_date == as.Date("2004-05-16"))
# acf1=ggAcf(HE["min_price"],200)
# acf2=ggAcf(HE["max_price"],200)
# acf3=ggAcf(HE["avg_price"],200)
# acf4=ggAcf(HE["coef_dist"],200)
# acf5=ggAcf(HE["sd_price"],200)
# ggarrange(acf1, acf2,acf3,acf4,acf5,
# ncol = 1, nrow = 5)
name2 =unique(df3$fuel)
df_acc_avg = data.frame(product=c(rep(NA,10)),err_type=c(rep(NA,10)),ME=c(rep(NA,10)),RMSE=c(rep(NA,10)),MAE=c(rep(NA,10)),MPE=c(rep(NA,10)),MAPE=c(rep(NA,10)))
for(i in 1:5){
c1 = i*2
c2 = i*2-1
gas = name2[i]
HE=df3[df3$fuel==gas,]
HE['group'] = c(rep(1,785-52),rep(2,52))
HE$start_date = as.Date( HE$start_date)
HE_1=HE[HE['group'] ==1,]
HE_2=HE[HE['group'] ==2,]
var.fit_HE = VAR(HE_1[,c(3:7)], 5, type = "trend", ic = "AIC",season=80)
summary(var.fit_HE)
# check residual
check_r=checkresiduals(residuals(var.fit_HE)[,3])
box = Box.test(residuals(var.fit_HE)[,3], type = "Ljung-Box")
print(box)
pred.var_HE <- predict(var.fit_HE,HE_1[,c(3:7)],n.ahead=52)
df_acc_avg[i,]=c(name[i],"train",accuracy(var.fit_HE$varresult[[3]])[1:5])
df_acc_avg[i+5,]=c(name[i],"test",accuracy(pred.var_HE$fcst[[3]][,1],HE_2$avg_price))
df_plotpred = data.frame(date=as.Date(HE$start_date),value = c(rep(NA,733),pred.var_HE$fcst[["avg_price"]][,1]))
df_plotpred['lower'] = c(rep(NA,733),pred.var_HE$fcst[["avg_price"]][,2])
df_plotpred['upper'] = c(rep(NA,733),pred.var_HE$fcst[["avg_price"]][,3])
vis.fit = ggplot() +
geom_line(data = HE,aes(start_date, avg_price),col=col_prod2[c1]) +
geom_line(data=df_plotpred,aes(date, value),col=col_prod2[c2])+
geom_ribbon(data = df_plotpred,aes(x = date, ymax = upper, ymin = lower), alpha = 0.5, fill = col_prod2[c2])+
rremove('xlab')+rremove("ylab")+theme_gray()
acf.fit=ggAcf(residuals(var.fit_HE)[,3],200)
assign(paste("vis", i, ".fit",sep = ""), vis.fit)
assign(paste("acf", i, ".fit",sep = ""), acf.fit)
assign(paste("checkr", i,sep = ""), check_r)
assign(paste("box", i,sep = ""), box)
}
##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 0.088645, df = 1, p-value = 0.7659
##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 0.000648, df = 1, p-value = 0.9797
##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 0.024801, df = 1, p-value = 0.8749
##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 0.0084985, df = 1, p-value = 0.9265
##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 9.0863e-05, df = 1, p-value = 0.9924ggarrange(acf1.fit, acf2.fit,acf3.fit,acf4.fit,acf5.fit,
ncol = 1, nrow = 5)
df_acc_avg[,-c(1,2)] <- sapply(df_acc_avg[,-c(1,2)],as.numeric)
print(df_acc_avg, digits = 2)## product err_type ME RMSE MAE MPE MAPE
## 1 Hydrous.Ethanol train 2.6e-05 0.013 0.0086 -0.00036 0.39
## 2 Regular.Gasoline train 1.4e-05 0.019 0.0097 -0.00152 0.32
## 3 Natural.Gas train 1.6e-04 0.243 0.1173 -0.00171 0.26
## 4 LPG train -6.0e-07 0.017 0.0125 -0.00749 0.68
## 5 Diesel train 1.9e-06 0.017 0.0093 -0.00254 0.40
## 6 Hydrous.Ethanol test -7.6e-02 0.107 0.0885 -2.25006 2.60
## 7 Regular.Gasoline test -2.2e-01 0.314 0.2635 -5.15340 5.99
## 8 Natural.Gas test -6.2e+00 6.792 6.2491 -8.66026 8.66
## 9 LPG test 2.5e-01 0.278 0.2532 7.92604 7.95
## 10 Diesel test 2.8e-02 0.109 0.0815 0.69713 2.21is.num <- sapply(df_acc_avg, is.numeric)
df_acc_avg[is.num] <- lapply(df_acc_avg[is.num], round, 4)
print(as.matrix(df_acc_avg))## product err_type ME RMSE MAE MPE
## [1,] "Hydrous.Ethanol" "train" " 0.0000" "0.0130" "0.0086" "-0.0004"
## [2,] "Regular.Gasoline" "train" " 0.0000" "0.0193" "0.0097" "-0.0015"
## [3,] "Natural.Gas" "train" " 0.0002" "0.2434" "0.1173" "-0.0017"
## [4,] "LPG" "train" " 0.0000" "0.0174" "0.0125" "-0.0075"
## [5,] "Diesel" "train" " 0.0000" "0.0175" "0.0093" "-0.0025"
## [6,] "Hydrous.Ethanol" "test" "-0.0758" "0.1072" "0.0885" "-2.2501"
## [7,] "Regular.Gasoline" "test" "-0.2237" "0.3139" "0.2635" "-5.1534"
## [8,] "Natural.Gas" "test" "-6.2491" "6.7924" "6.2491" "-8.6603"
## [9,] "LPG" "test" " 0.2526" "0.2781" "0.2532" " 7.9260"
## [10,] "Diesel" "test" " 0.0281" "0.1087" "0.0815" " 0.6971"
## MAPE
## [1,] "0.3914"
## [2,] "0.3233"
## [3,] "0.2612"
## [4,] "0.6777"
## [5,] "0.3953"
## [6,] "2.6028"
## [7,] "5.9929"
## [8,] "8.6603"
## [9,] "7.9479"
## [10,] "2.2119"print(box1)##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 0.088645, df = 1, p-value = 0.7659print(box2)##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 0.000648, df = 1, p-value = 0.9797print(box3)##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 0.024801, df = 1, p-value = 0.8749print(box4)##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 0.0084985, df = 1, p-value = 0.9265print(box4)##
## Box-Ljung test
##
## data: residuals(var.fit_HE)[, 3]
## X-squared = 0.0084985, df = 1, p-value = 0.9265ggarrange(vis1.fit, vis2.fit,vis3.fit,vis4.fit,vis5.fit, labels = c("Hydrous Ethanol", "Regular Gasoline","LPG","Natural Gas","Diesel"), ncol = 3, nrow = 2, font.label = list(size = 10, face = "bold"))
EDA *2
library(ggplot2)
library(forecast)
theme_set(theme_classic())
# Plot each product's price per year
library(RColorBrewer)
col_prod = brewer.pal(15,"BrBG")
brks = df5_scaled$date[seq(1, length(df5_scaled$date),52)]
lbls = unique(lubridate::year(df5_scaled$date))
df3_plot = df3
df3_plot['year']=lubridate::year(df3$start_date)
df3_plot['month']=month.abb[lubridate::month(df3$start_date)]
df3_plot$year=as.factor(df3_plot$year)
name2 =unique(df3_plot$fuel)
for(i in 1:5){
gas = name2[i]
vis=ggplot(df3_plot[df3_plot$fuel==gas,])+
geom_line(aes(x=month,y=scale(avg_price),group=year,col=year))+
rremove('xlab')+rremove("ylab")
theme_gray()# title
assign(paste("viss", i,sep = ""), vis)}
ggarrange(viss1, viss2,viss3,viss4,viss5, labels = c("Hydrous Ethanol", "Regular Gasoline","LPG","Natural Gas","Diesel"), ncol = 2, nrow = 3, font.label = list(size = 10, face = "bold"))